Light and Geometric Optics Study Guide

Electromagnetic Waves and Applications

• Matching Electromagnetic Waves with Related Terms:

  • X-rays: Associated with cancer treatment (linked to item [ a ] in the transcript).

  • Ultraviolet Light: Associated with baggage screening (linked to item [ b ] in the transcript).

  • Radio Waves: Associated with telecommunications (linked to item [ c ] in the transcript).

  • Infrared Light: Associated with DVD player remote controls (linked to item [ d ] in the transcript).

  • Microwaves: Associated with radar (linked to item [ e ] in the transcript).

  • Gamma Rays: Associated with Vitamin D production (linked to item [ f ] in the transcript).

  • Visible Light: Associated with theatre/concert effects (linked to item [ g ] in the transcript).

General Optics Vocabulary

• Light Ray: A line on a diagram representing the direction and path that light is travelling.

• Geometric Optics: The use of light rays to determine how light behaves when it strikes objects (or an object).

• Incident Light: The light emitted from a source that strikes an object.

• Incident Ray: The incoming ray that strikes a surface.

• Reflected Ray: The ray that bounces off a reflective surface.

• Image: The reproduction of an object through the use of light.

• Mirror: Any polished surface reflecting an image.

• Reflection: The bouncing back of light from a surface.

• Medium: Any physical substance through which energy can be transferred.

• Radiation: A method of energy transfer that does not require a medium; the energy travels at the speed of light.

• Visible Light: The electromagnetic waves that the human eye can detect.

• Electromagnetic Spectrum: The classification of electromagnetic waves by energy.

Light and Matter Interaction

• Transparent: A material that transmits all or almost all incident light; objects can be clearly seen through the material.

• Translucent: A material that transmits some incident light but absorbs or reflects the rest; objects are not clearly seen through the material.

• Opaque: A material that does not transmit any incident light; all incident light is either absorbed or reflected; objects behind the material cannot be seen at all.

Mathematical and Geometric Relationships in Optics

• Angle of Incidence: The angle between the incident ray and the normal.

• Angle of Refraction: Defined in the quiz as the angle between the reflected ray and the normal.

• Critical Angle: The angle of incidence that results in an angle of refraction of $90^\circ$.

• Total Internal Reflection: The situation occurring when the angle of incidence is greater than the critical angle.

• Normal: An imaginary line drawn at a $90^\circ$ angle (perpendicular) to the surface where the incident ray strikes.

• Index of Refraction ($n$): A number indicating how much light slows down when entering a material compared to its speed in space (vacuum). It is a dimensionless quantity because it is calculated by dividing one speed by another, causing the units ($\text{m/s}$) to cancel out.

Lens Terminology

• Converging Lens: A lens that is thickest in the middle and causes incident parallel light rays to converge through a single point after refraction.

• Diverging Lens: A lens that is thinnest in the middle and causes incident parallel light rays to spread apart after refraction.

• Optical Centre: The point at the exact centre of the lens.

• Principal Focus: The point on the principal axis of a lens where light rays parallel to the principal axis converge after refraction.

Methods of Light Production

• Luminous: An object that produces its own light.

• Non-luminous: An object that does not produce its own light.

• Incandescence: The production of light as a result of high temperature.

• Electric Discharge: The process of producing light by passing an electric current through a gas.

• LED (Light Emitting Diode): Light produced as a result of an electric current flowing only in one direction.

• Phosphorescence: The process of producing light by the absorption of UV light, resulting in the emission of visible light over an extended period of time.

• Fluorescence: The immediate emission of visible light as a result of the absorption of UV light.

• Chemiluminescence: The production of light as a result of a chemical reaction with little or no heat produced.

• Bioluminescence: The production of light in living organisms as the result of a chemical reaction with little or no heat produced.

• Triboluminescence: The production of light from friction as a result of scratching, crushing, or rubbing certain crystals.

Principles and Application Scenarios

• Convex Mirrors in Parking Garages:

  • Reasoning: These mirrors bulge outward, providing drivers with a much wider field of view than a standard flat mirror. This allows drivers to see around blind, sharp corners to prevent collisions.

  • Additional Uses: Side mirrors on cars (often marked with "objects in mirror are closer than they appear"), security mirrors in store corners to monitor for shoplifting, and small mirrors on ATMs to detect anyone standing behind the user.

• Laws of Reflection:

  • The incident ray, the reflected ray, and the normal line all lie on the same flat surface (plane).

  • The angle of incidence is exactly equal to the angle of reflection (Angle In = Angle Out).

• Image Characteristics for a Concave Mirror:

  • Scenario: Focus ($f$) = $75\,\text{cm}$; Object distance ($d_o$) = $60\,\text{cm}$.

  • Analysis: Since the object is placed inside the focal point (closer than typical focal distance), the resulting image is:

    • Larger (magnified).

    • Upright (right side up).

    • Located behind the mirror.

    • Virtual (cannot be projected onto a screen).

• Laundry Detergent and Optical Brighteners:

  • Companies claim detergents make clothes "brighter," which can be considered false advertising regarding actual cleanliness.

  • Mechanism: Detergents contain chemicals called optical brighteners that adhere to fabrics. These chemicals absorb invisible UV light from the sun and emit blue light (fluorescence). This makes clothes appear whiter and brighter to the human eye, even if dirt has not been removed more effectively than other detergents.

• Light Bending Behavior:

  • If light travels faster in a medium, it bends away from the normal line.

  • If light travels slower in a medium, it bends toward the normal line.

• Total Internal Reflection in Objects:

  • Diamonds: Diamonds exhibit intense sparkle due to a very high index of refraction and a very small critical angle ($\approx 24^\circ$). Light enters and hits the internal edges at angles wider than the critical angle, causing it to bounce inside (like a pinball) before exiting through the top.

  • Triangular Prisms: Glass has a critical angle of approximately $41^\circ$. When light enters a prism and strikes an internal wall at a $45^\circ$ angle, total internal reflection occurs because the incident angle exceeds the critical angle. This causes the prism to act as a perfect mirror.

Calculations and Quantitative Data

• Index of Refraction for Vinegar:

  • Speed of light in space ($c$): $3.00 \times 10^8\,\text{m/s}$

  • Speed of light in vinegar ($v$): $2.30 \times 10^8\,\text{m/s}$

  • Formula: $n = \frac{c}{v}$

  • Calculation: $n = \frac{3.00 \times 10^8}{2.30 \times 10^8} = 1.30$

• Index of Refraction for Fluorite:

  • Speed of light in fluorite ($v$): $2.10 \times 10^8\,\text{m/s}$

  • Formula: $n = \frac{3.00 \times 10^8}{v}$

  • Calculation: $n = \frac{3.00 \times 10^8}{2.10 \times 10^8} = 1.43$

• Total Internal Reflection Thresholds (Sapphire):

  • Critical Angle for Sapphire: $34.4^\circ$

  • Angle of incidence $23.7^\circ$: No (Too small, just refracts out).

  • Angle of incidence $34.7^\circ$: Yes (Bigger than $34.4^\circ$).

  • Angle of incidence $53.4^\circ$: Yes (Bigger than $34.4^\circ$).

  • Angle of incidence $31.5^\circ$: No (Too small, just refracts out).

• Lens Problem Setup:

  • Converging Lens:

    • Focal length ($f$) = $16\,\text{cm}$

    • Insect location ($d_o$) = $11\,\text{cm}$

    • Current problem status: Requires calculation to locate the image position ($d_i$).